This is the preprint version of the contribution published as:
Knapp, N., Fischer, R., Huth, A. (2018):
Linking lidar and forest modeling to assess biomass estimation across scales and disturbance states
Remote Sens. Environ. 205 , 199 – 209
The publisher’s version is available at:
http://dx.doi.org/10.1016/j.rse.2017.11.018
1 Title:
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Linking lidar and forest modeling to assess biomass estimation across scales and disturbance states 2
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List of authors:
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Nikolai Knapp1, Rico Fischer1, Andreas Huth1, 2, 3 5
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Authors’ affiliation:
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1) Department of Ecological Modeling, Helmholtz Centre for Environmental Research (UFZ), 04318 8
Leipzig, Germany 9
2) German Centre for Integrative Biodiversity Research (iDiv), Halle-Jena-Leipzig, 04103 Leipzig, Germany 10
3) Institute for Environmental Systems Research, Department of Mathematics/Computer Science, 11
University of Osnabrück, 49076 Osnabrück, Germany 12
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Corresponding author:
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Nikolai Knapp, Email: nikolai.knapp@ufz.de), Tel.: +49 3412354764 15
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Type of paper:
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Primary Research Article 18
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2 Abstract
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Light detection and ranging (lidar) is currently the state-of-the-art remote sensing technology for 23
measuring the 3D structures of forests. Studies have shown that various lidar-derived metrics can be 24
used to predict forest attributes, such as aboveground biomass. However, finding out which metric 25
works best at which scale and under which conditions requires extensive field inventories as ground- 26
truth data. The goal of our study was to overcome the limitations of inventory data by complementing 27
field-derived data with virtual forest stands from a dynamic forest model. The simulated stands were 28
used to compare 29 different lidar metrics for their utility as predictors of tropical forest biomass at 29
different spatial scales. We used the process-based forest model FORMIND, developed a lidar simulation 30
model, based on the Beer-Lambert law of light extinction, and applied it to a tropical forest in Panama.
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Simulation scenarios comprised undisturbed primary forests and stands exposed to logging and fire 32
disturbance regimes, resulting in mosaics of different successional stages, totaling 3.7 million trees on 33
4,200 ha. The simulated forest was sampled with the lidar model. Several lidar metrics, in particular 34
height metrics, showed good correlations with forest biomass, even for disturbed forest. Estimation 35
errors (nRMSE) increased with decreasing spatial scale from < 10% (200-m scale) to > 30% (20-m scale) 36
for the best metrics. At the often used 1-ha scale, the top-of-canopy height obtained from canopy height 37
models with fine to relatively coarse pixel resolutions (1 to 10 m) yielded the most accurate biomass 38
predictions, with nRMSE < 6% for undisturbed and nRMSE < 9% for disturbed forests. This study 39
represents the first time dynamic modeling of a tropical forest has been combined with lidar remote 40
sensing to systematically investigate lidar-to-biomass relationships for varying lidar metrics, scales and 41
disturbance states. In the future, this approach can be used to explore the potential of remote sensing of 42
other forest attributes, e.g., carbon dynamics, and other remote sensing systems, e.g., spaceborne lidar 43
and radar.
44
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Keywords: aboveground biomass; tropical forest; disturbance; lidar simulation; forest modeling;
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resolution; scale 46
4 1. Introduction
47 48
Due to their important role in the global carbon cycle and ongoing deforestation and degradation, 49
tropical forests are of particular interest to biomass remote sensing. Tropical forest carbon accounting 50
and monitoring of deforestation are important tasks in the context of REDD+ and global climate 51
modeling. In recent years, remote sensing has led to considerable improvements in this field (Gibbs et 52
al., 2007; De Sy et al., 2012; Pan et al., 2013). Airborne small-footprint lidar (light detection and ranging) 53
is currently the state-of-the-art technology for measuring the 3D structure of forests (Lefsky et al., 54
2002b; Wulder et al., 2012; Mascaro et al., 2014). Various lidar metrics correlate well with different 55
forest attributes. In particular, lidar-derived height metrics have commonly been used to predict forest 56
aboveground biomass (AGB) and carbon density (ACD) (Drake et al., 2002; Asner et al., 2009; Dubayah et 57
al., 2010; Jubanski et al., 2013; Asner & Mascaro, 2014).The major challenges in biomass estimation 58
based on lidar data are that 1) the calibration of the prediction functions relies on field data that must be 59
collected manually in inventory plots; and 2) there are many different metrics available using different 60
spatial scales, and the task is to find the combination that provides accurate AGB predictions.
61
In inventory plots, tree diameters at breast height (DBH) are typically measured, from which AGB is 62
calculated via known allometric equations (e.g., Chave et al., 2005, 2014; Chen 2015). Lidar data are 63
acquired for the same inventory plots to build regression models between lidar-based structure metrics 64
and ground-based AGB. A wide range of metrics can be calculated from lidar data. To date, no standard 65
approach for AGB estimation from lidar has been established and different studies have applied different 66
metrics (Chen 2013; Lu et al. 2014). Several publications have compared metrics among each other for 67
different forest types (e.g., Lefsky et al., 1999, 2002a; Dubayah et al., 2010; Jubanski et al., 2013).
68
However, there has not been a comparison of a wide range of metrics on a single tropical forest dataset.
69
Lidar metrics can generally be divided into metrics which are based on the full 3D point cloud of lidar 70
5
returns and metrics which are based on canopy height models (CHM), i.e., the rasterized canopy surfaces 71
which are derived from the uppermost returns of the point clouds (Chen 2013). The full 3D point cloud 72
contains more information about the vertical canopy structure than the corresponding CHM. On the 73
other hand, the vertical distribution of lidar returns also depends on technical properties of the specific 74
sensor, making point-cloud-based metrics less robust and comparable between different studies than 75
CHM-based metrics (Næsset, 2009; Asner & Mascaro, 2014). Many commonly used metrics can be 76
calculated based on both types of data. Those metrics include mean heights (Lefsky et al., 2002a; Asner 77
& Mascaro, 2014), relative height quantiles (the heights below which a certain percentage of returns or 78
pixels falls) (Patenaude et al., 2004; Dubayah et al., 2010; Meyer et al., 2013), and metrics of 79
heterogeneity such as the standard deviation of heights or the Shannon diversity index of the height 80
profiles (Stark et al., 2012). Other metrics, such as the ratio of above ground returns to total returns or 81
fractional canopy cover above a certain height, that can be derived either from point clouds or CHMs 82
describe relative vegetation cover.
83
An important aspect of AGB prediction from remote sensing is spatial resolution. Resolution means, first, 84
spatial resolution of the remote sensing data from which different metrics are calculated and, second, 85
the spatial resolution of the output map, i.e., the grain size of the units for which the metrics are 86
calculated to produce an AGB prediction. The resolution of the data is determined by the sensor’s 87
technical specifications and the capacities to store and process data. The resolution of the mapping units 88
is influenced by the desired estimation accuracy and the desired spatial detail of the mapped product.
89
Köhler & Huth (2010), Mascaro et al. (2011b) and Chen et al. (2016) showed how errors in AGB 90
estimations from mean lidar heights decreased with increasing grain sizes and that a grain of 91
approximately 1 ha is required to achieve errors of < 10%.
92
Fitting any of the described lidar metrics to measured AGB relies on field inventory data. Forest 93
inventory plots are limited in number, size and structural variety. The collection of inventory data is 94
6
costly and laborious and most studies in the past made use of tens to a few hundred plots (Fassnacht et 95
al., 2014). Those plots are often located in old growth forests. Hence, available data sets might not cover 96
the full structural complexity of forests over their entire successional range (noteworthy exceptions are 97
e.g., Dubayah et al. 2010, Poorter et al. 2016). For lidar-to-AGB-calibration, a broad range of different 98
forest succession states that cover the range of all possible AGB stocks and associated forest structures is 99
preferable. To overcome this limitation, we propose a new approach in which we complement in situ 100
measurements with simulated forest stands (Fig. 1). We used an individual-based forest model 101
(FORMIND, Fischer et al., 2016) to simulate a large virtual inventory dataset, covering the full range of 102
succession stages by including forest disturbances in the simulations. The model was parameterized to 103
represent the well-studied lowland tropical rainforest of Barro Colorado Island, Panama (Condit et al., 104
2001; Kazmierczak et al., 2014). We developed a lidar model to sample lidar data of simulated forest 105
stands.
106
7 107
Fig. 1: Workflow of the study. Reference data from field inventories and an airborne lidar campaign were used to
108
parameterize and calibrate a forest model and a lidar model. With the models, large quantities of simulated inventory and
109
simulated lidar data were generated, allowing for a systematic analysis of lidar-to-biomass relationships under different
110
disturbance regimes and for various spatial scales.
111
The research goals of this study were 1) to establish a lidar simulation model that is able to produce 112
synthetic lidar-like data for dynamic forest model output; 2) to test a wide variety of lidar metrics for 113
their ability to predict AGB of a tropical rainforest at various spatial scales; and 3) to investigate the 114
influence of disturbances on the lidar-to-biomass relationships.
115 116
8 2. Material & Methods
117 118
2.1 Study area 119
The study focused on the tropical forest on Barro Colorado Island (BCI), Panama (9.15° N, 79.85° W). BCI 120
is a 15 km2 island located in Lake Gatun, an artificial water body created by the construction of the 121
Panama Canal (Condit et al., 2001). It is covered with semi-deciduous tropical lowland rainforest, the 122
minimum forest age is estimated to range from 300 to 1500 years (Bohlman & O’Brien, 2006; Meyer et 123
al., 2013; Lobo & Dalling, 2014). The climate is characterized by average daily maximum and minimum 124
temperatures of 30.8 and 23.4 °C and an annual precipitation sum of approximately 2600 mm, with a dry 125
season from January to April (Condit et al., 2001). A 50-ha rainforest observation plot is located on the 126
central plateau of the island, with terrain altitudes varying between 120 and 160 m above sea level (Lobo 127
& Dalling, 2014). Since the establishment of the plot in the early 1980s, each tree in the 1000 m × 500 m 128
area with a DBH ≥ 1 cm has been measured during censuses in five year intervals (Condit, 1998; Hubbell 129
et al., 1999, 2005). Estimates of the mean canopy height are 24.6 ± 8.2 m, and those of the mean AGB 130
are 281 ± 20 t/ha (Chave et al., 2003).
131 132
2.2 Lidar data 133
An airborne discrete point cloud lidar dataset was collected on BCI in August 2009 with a multi-pulse 134
scanning laser altimeter (Optech ALTM Gemini system; BLOM Sistemas Geoespaciales SLU, Madrid, 135
Spain, Lobo & Dalling, 2014). The terrain elevation was subtracted from the point cloud to obtain the 136
relative height above ground. Point densities ranged from 0 to 60 m-2 with a median of 10 m-2 and a 5th- 137
percentile of 4 m-2. To avoid locally varying point densities, caused by flight swath overlaps, the point 138
clouds were thinned by random subsampling of 4 returns in each square meter. A 1-m resolution canopy 139
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height model (CHM) was derived from the highest returns in each square meter. Data processing was 140
performed using LAStools (Isenburg, 2011) and R (R Development Core Team, 2014).
141 142
2.3 Lidar model description 143
The purpose of the lidar model is the simulation of a lidar scan of a given forest stand. More specifically, 144
it generates point clouds of discrete returns as usually produced by small-footprint lidar systems. As 145
input, a tree list has to be provided. The list can either be real forest inventory data or data generated by 146
a forest model (Fig. 2a). The basic elements of the model are trees, lidar pulses and lidar returns. Trees 147
are characterized by their position (X- and Y-coordinate), height, crown length, crown radius, crown 148
shape and leaf area index (LAI). The model operates in a 3D space represented by an array of cuboid 149
voxels. Each vertical column of voxels represents one modeled lidar pulse. Lidar returns are points in 3D 150
space, characterized by their X-, Y- and Z-coordinates.
151
From the tree list, a voxel representation of the entire forest is created. Thus, voxels that could 152
potentially produce a lidar return, because they belong to a tree crown or the ground, are distinguished 153
from empty space voxels. The voxel forest is then scanned with a virtual lidar. The simulation follows a 154
probabilistic approach. Instead of explicitly simulating the branches and foliage and their interaction with 155
laser beams within the tree crowns, the model assumes that the tree crown space is a homogeneous, 156
turbid medium filled with a certain leaf area density (LAD). The probability of having a lidar return from a 157
certain point decreases as the distance the laser beam has to travel through the medium before reaching 158
the point increases. This relationship is analogous to the Beer-Lambert light-extinction law (Campbell &
159
Norman, 2012). Thus, the probability for a lidar return P for each tree and ground voxel (Fig. 2c) can be 160
calculated as a function of cumulative leaf area index LAI above the voxel (Fig. 2b).
161
𝑷(𝑳𝑨𝑰) = 𝑷𝟎 ∙ 𝒆−𝒌 ∙𝑳𝑨𝑰 (1)
162
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P0 in Eq. (1) represents the probability of obtaining a return from the very upper voxel, where the laser 163
beam hits a tree or the ground for the first time. The parameter k is the exponential extinction 164
coefficient, which determines how fast the return probability decreases after entering the crown space.
165
The decision regarding whether each voxel will contain a return is taken stochastically, based on the 166
calculated return probability. Ultimately, this leads to a discrete point cloud (Fig. 2d). The voxel 167
resolution was set to 0.5 m × 0.5 m along the horizontal direction and 1 m along the vertical direction.
168
The parameters P0 and k were calibrated such that simulated point cloud profiles derived for subareas of 169
the 50-h inventory data set matched the airborne lidar profiles of those subareas (details see 170
supplements). The resulting value for k = 0.2 can be confirmed by literature (Campbell & Norman 2012, 171
Jones 2013). For P0 we found 0.2 to be a good value, leading to simulated point densities that were 172
similar to the airborne reference point cloud. P0 being smaller than 1 can be interpreted by the 173
heterogeneity of leafs, branches and empty space within the tree crown. This means that a laser beam 174
entering the idealized cylindrical tree crown does not necessarily trigger a return in the first voxel.
175
11 176
Fig. 2: Principle of the lidar model. Inputs to the workflow can either be forest model output or field inventory data. The
177
pictures on the right side show intermediate products: a) Visualization of a forest stand; b) voxel representation with colors
178
indicating the cumulative leaf area index; c) voxel representation with colors indicating the probability of containing a lidar
179
return; d) simulated lidar point cloud with colors indicating height above ground.
180 181
12 2.4 Forest model description
182
FORMIND belongs to the group of forest gap models (Botkin et al., 1972; Shugart, 1984; Bugmann, 183
2001). As such, the model simulates the processes of establishment, growth, competition and mortality 184
of trees on spatial patches with the dimensions of a typical treefall gap (20 m × 20 m). By combining 185
many patches, large forest areas of hundreds of hectares can be simulated. FORMIND is an individual- 186
based model (IBM) in which the individuals represent trees that belong to different plant functional 187
types (PFTs). One PFT may contain several species with similar ecological traits. FORMIND has been 188
applied to many tropical forest sites and has proven capable of accurately reproducing patterns 189
observed in these complex ecosystems (Fischer et al., 2016). The individual-based model architecture 190
allows for the inclusion of disturbances such as logging or forest fires in a structurally realistic way. A 191
detailed description of FORMIND including the modules for logging and fire disturbance can be found in 192
Fischer et al. (2016). The supplements contain descriptions of the parameterization of the lidar model 193
and the forest model (Tab. S1). Before using the forest model output for remote sensing analyses, the 194
structural validity of the simulated old growth stands was confirmed by visually comparing biomass 195
stocks (Fig. S1) and stem size distributions (Fig. S2) of all PFTs to the values obtained from the inventory 196
data.
197 198
2.5 Simulation experiment 199
Using FORMIND, we simulated the development of a 16 ha (400 m × 400 m) area of the BCI forest over 200
several thousands of years and stored the results at 20-yr intervals. The simulations were repeated with 201
different disturbance regimes. The first run comprised 2000 yr without any external disturbance, 202
simulating only natural gap dynamics. In the second run, forest fires were introduced as a source of 203
spatially heterogeneous disturbance to clear parts of the area regularly and enable natural succession 204
and regrowth. Fire occurrence was drawn from a Poisson distribution such that the mean interval 205
13
between two fire events was 25 yr. Fire size at each fire event was drawn from an exponential 206
distribution, such that on average 50% of the total area was affected. More information on the fire 207
module used is provided in Fischer (2013) and Fischer et al. (2016). The third scenario included selective 208
logging. At a logging cycle of 99 yr, all trees with DBH > 30 cm were felled and removed. More 209
information on the logging module used is provided in Huth et al. (2004). For all three runs, the first 200 210
yr were discarded as spin-up. For each of the remaining simulation years, a virtual lidar campaign using 211
the lidar model was conducted. The disturbance frequencies and intensities were not intended to 212
represent realistic disturbances scenarios in the study region. The intention was to sample many stands 213
at each stage along the full successional range, using the disturbance modules to regularly set the forest 214
back to an early stage. The selective logging acts on the whole area, while the fires move in a spatially 215
explicit way through the simulated area, causing mosaics of unaffected forest next to cleared areas 216
where succession starts over. Such patchy landscapes are typical for many forest regions, although the 217
reasons for the structures may be as diverse as clear cuts, wind blowdowns, fires or natural areas 218
without vegetation, e.g., grasslands or water bodies. Thus, these simulations produce landscapes that 219
can be used as general examples of heterogeneous landscapes.
220 221
2.6 Lidar-based biomass prediction 222
We analyzed forest plots measuring 20, 33, 50, 100 or 200 m (side length). At each spatial scale, a range 223
of 29 different lidar metrics (Tab. 1) were tested for their suitability as single predictors of AGB. Metrics 224
were either derived from point clouds (PC) or canopy height models (CHM). CHMs were constructed 225
from point clouds by rasterizing the highest lidar returns in each pixel of a given pixel size.
226
Point-cloud-based metrics comprised the mean canopy profile height (MCH), which is the mean height of 227
all lidar returns, and the quadratic mean canopy profile height (QMCH), where high returns receive a 228
14
larger weighting than low returns. For a given point cloud profile pPC that consists of lidar return counts 229
at height bins hi, MCH and QMCH can be calculated from Eq. (2) and (3), respectively.
230
𝑴𝑪𝑯 = ∑𝒊𝒎𝒂𝒙𝒊=𝟏∑ (𝒑𝑷𝑪,𝒊𝒑 ∙ 𝒉𝒊)
𝑷𝑪,𝒊 𝒊𝒎𝒂𝒙𝒊=𝟏
231 (2)
𝑸𝑴𝑪𝑯 = √∑𝒊𝒎𝒂𝒙𝒊=𝟏∑ (𝒑𝑷𝑪,𝒊𝒑 ∙ 𝒉𝒊𝟐)
𝑷𝑪,𝒊 𝒊𝒎𝒂𝒙𝒊=𝟏
(3)
232
where pPC,i is the lidar return counts in height bin hi. A metric similar to MCH can be derived from the 233
vertical CHM profile instead of the point cloud profile. This metric corresponds to the mean of all pixel 234
values of the CHM, and is commonly referred to as the mean top-of-canopy height (TCH, Eq. (4)).
235
𝑻𝑪𝑯 = ∑𝒊𝒎𝒂𝒙𝒊=𝟏∑ (𝒑𝑪𝑯𝑴,𝒊𝒑 ∙ 𝒉𝒊)
𝑪𝑯𝑴,𝒊 𝒊𝒎𝒂𝒙𝒊=𝟏
236 (4)
Because a CHM can be derived from a point cloud at variable pixel resolutions, by taking the height of 237
the highest return that falls into each pixel, TCH always depends on the pixel size used. We calculated 238
TCH from CHMs with pixel side lengths of 1, 5, 10, 20, 33, 50 and 100 m. Note that, once the pixel size 239
equals the plot size for which AGB is calculated, TCH is equal to the maximal height in the plot, which is 240
also referred to as Hmax or RH100 in the literature. Another method for measuring forest height from 241
lidar data is by using relative height quantiles of either the point cloud or the CHM. These quantiles 242
represent the heights below which a certain percentage of the returns or CHM pixels fall. We calculated 243
RH25, RH50 and RH75 for the point clouds and 1-m resolution CHMs.
244
Other metrics, however, capture the vertical heterogeneity of the forest. Those metrics include the 245
standard deviation (SD) of heights (point-cloud- or CHM-based), the coefficient of variation (CV, Eq. (5) 246
and (6)), the skewness of the vertical point cloud profile (Eq. (7), where N is the total number of points 247
and hi is the height of each point i), the Shannon Index (Eq. (8), where imax is the number of height layers 248
and pi is the count of points in the layer i) as a measure of entropy of the profile and the P:H ratio (Eq.
249
(9), where imax is the number of height layers, pi is the count of points in the layer i and hi is height of 250
15
layer i), which describes the height of the densest part of the point cloud (peak in the profile) relative to 251
the maximal height (Marvin et al., 2014).
252
𝑪𝑽𝑷𝑪= 𝑺𝑫𝑴𝑪𝑯𝑷𝑪 (5)
253
𝑪𝑽𝑪𝑯𝑴= 𝑺𝑫𝑻𝑪𝑯𝑪𝑯𝑴 (6)
254
𝑺𝒌𝒆𝒘𝒏𝒆𝒔𝒔 = 𝑵𝟏 ∙ ∑ (𝒉𝒊𝑺𝑫−𝑴𝑪𝑯
𝑷𝑪 )𝟑
𝑵𝒊=𝟏 (7)
255
𝑺𝒉𝒂𝒏𝒏𝒐𝒏 𝑰𝒏𝒅𝒆𝒙 = − ∑𝒊𝒊=𝟏𝒎𝒂𝒙𝒑𝒊 ∙ 𝐥𝐧(𝒑𝒊) (8)
256
𝑷: 𝑯 𝒓𝒂𝒕𝒊𝒐 = 𝒉( 𝐦𝐚𝐱𝒊 𝝐 [𝟏, 𝒊𝒎𝒂𝒙](𝒑𝒊))
𝒊 𝝐 [𝟏, 𝒊𝒎𝒂𝒙]𝐦𝐚𝐱 (𝒉𝒊) (9)
257
Furthermore, we calculated vegetation density metrics. Based on the point clouds, the count of 258
aboveground returns divided by either the count of ground returns NAGR/NGR or the count of total returns 259
NAGR/NTR was calculated. Based on the CHMs, the fractional canopy cover (FCC) was derived by defining 260
different height thresholds below which a CHM-pixel was considered a canopy gap. We calculated FCC0, 261
FCC10 and FCC20 using the forest floor, 10 m and 20 m as height thresholds, respectively.
262
Tab. 1: List of the lidar metrics and the underlying data (PC = point cloud, CHM = canopy height model). CHM usually refers to
263
1-m resolution rasters, except for TCH where various resolutions were tested.
264
Lidar metric Description Data
MCH Mean canopy profile height PC
QMCH Quadratic mean canopy profile height PC
TCH Mean top-of-canopy height (at variable CHM pixel resolutions), e.g., TCH5 is based on 5-m pixels
CHM RH Relative height quantile, e.g., RH50 is the 50-percentile of
heights
PC or CHM
SD Standard deviation of heights PC or CHM
CV Coefficient of variation of heights (normalized SD) PC or CHM
Skewness Skewness of the vertical profile PC
Shannon Index Entropy of the vertical profile PC
P:H ratio Relative height of the peak in the vertical profile PC NAGR/NGR Ratio of aboveground returns to ground returns PC NAGR/NTR Ratio of aboveground returns to total returns PC FCC Fractional canopy cover, e.g., FCC10 is the relative share of pixels
higher than 10 m
CHM 265
16
Each lidar metric LM was fit to the dependent variable AGB using a power law model (Eq. (10)) and 266
maximum likelihood estimation in R.
267
𝑨𝑮𝑩 = 𝒂 ∙ 𝑳𝑴 𝒃 (10)
268
If possible, such relationships were derived for plots with side lengths of 20, 33, 50, 100 and 200 m.
269
Relationships could not be derived in cases where pixel size exceeded plot size or where the maximum 270
likelihood estimation did not provide a parameter b different from zero. The AGB-prediction accuracy for 271
the different power law functions was quantified as the normalized root mean square error (nRMSE) [%].
272
The measure was calculated as the RMSE of n AGB predictions against n observations, normalized by the 273
mean observed AGB (Eq. (11)).
274
𝒏𝑹𝑴𝑺𝑬 = √∑ (𝒑𝒓𝒆𝒅𝑨𝑮𝑩𝒏𝒊=𝟏 𝒏𝒊−𝒐𝒃𝒔𝑨𝑮𝑩𝒊)𝟐 ∙ 𝒐𝒃𝒔𝑨𝑮𝑩̅̅̅̅̅̅̅̅̅̅̅𝟏 (11)
275
The power law parameters and additional statistics (mean, RMSE, bias, R², slope and intercept of linear 276
fits between predictions and observations) for all metrics, scales and datasets (672 models) can be found 277
in Tab. S2.
278 279
17 3. Results
280 281
3.1 Forest and lidar simulation results 282
The forest simulations could reproduce AGB succession over time for the four PFTs. An overshoot of total 283
AGB around a forest age of 100 yr was observed (Fig. S1). The duration of the primary succession and the 284
biomass overshoot are consistent with observations by Mascaro et al. (2012). Furthermore, the stem size 285
distributions for all four PFTs matched well between the model and reference data (Fig. S2). The AGB 286
distributions of reference data and undisturbed and disturbed FORMIND runs can be found in Fig. 3, and 287
for the undisturbed case, the simulated distributions are in good agreement with previously reported 288
distributions based on field data (Chave et al., 2003). At all scales the range of AGB in undisturbed 289
simulations was smaller than the observed range of AGB in the field reference data. In the disturbance 290
scenarios, the range of AGB values increased. At the small 20 m × 20 m scale, the real forest contained 291
extremely high local AGB values (max. 2022 t/ha) caused by single large trees. Such extreme values were 292
not reached in the simulations.
293
294
Fig. 3: Relative frequency distributions of aboveground biomass (AGB). Columns represent the BCI field data (50 ha) and
295
output of FORMIND simulations from different disturbance scenarios (1,400 ha each). Rows represent different spatial
296
resolutions. Notice the different axis scaling in each row.
297
18 298
Using the lidar simulation approach, synthetic lidar data were generated for the simulated forest stands.
299
Lidar simulation outputs, such as the vertical point cloud profile (Fig. 4) and CHMs, closely resembled 300
their airborne equivalents. In the supplements we present how alternative assumptions about the tree 301
geometry affect the simulated lidar profiles and metrics (Fig. S15 to S18).
302 303
304
Fig. 4: Vertical lidar profiles of a) the 9 ha in the southwestern corner of the BCI megaplot, airborne and simulated based on
305
inventory data; b) the same for the 9 ha in the northeastern corner of the BCI megaplot; and c) the simulated lidar profile of
306
16 ha simulated forest in FORMIND in the old growth stage (age 500 yr). Dashed lines mark the mean canopy profile height
307
(MCH), and ‘×’ symbols mark the ground return peaks.
308 309
3.2 Biomass prediction from top-of-canopy height 310
Based on the simulated stands, we analyzed 4,200 ha of forest (3.7 million trees with DBH ≥ 3 cm) with 311
respect to the relationships between forest height (TCH) and biomass (AGB). We generated undisturbed 312
(1,400 ha), fire-disturbed (1,400 ha) and logging-disturbed (1,400 ha) stands. Fig. 5 shows the 313
relationships observed for different plot sizes (20 to 100 m) assuming a fine resolution (pixel size = 1 m).
314
The disturbed stands (fire and logging were pooled) cover a wider range of TCH and AGB values than the 315
19
undisturbed stands. The fitted relationships for undisturbed and disturbed forest stands are similar. The 316
scattering around the regression lines decreases with increasing plot size. If we decrease the pixel 317
resolution from 1 to 10 m (Fig. 6), we observe a change in the TCH-to-AGB relationship. Curves become 318
flatter because averaging over lidar point height maxima in 10 m × 10 m pixels leads to higher TCH- 319
values than averaging over the lidar point height maxima in all 1 m × 1 m pixels. Thus, the coarser the 320
pixel resolution is, the higher the TCH value for a given stand becomes. For the 1-m and the 10-m pixel 321
resolution, we observe similar relations for disturbed and undisturbed forests, respectively. More 322
extensive analyses and graphics that consider the BCI reference data and treat the different disturbance 323
regimes separately can be found in the supplementary material (Fig. S4 and following).
324
20 325
Fig. 5: Aboveground biomass (AGB) as a function of top-of-canopy height (TCH) from 1-m pixel resolution (CHM) for different
326
plot sizes. All data was derived from FORMIND and lidar simulations. 1) The first row demonstrates the sampling approach.
327
Shown is a scene of 9 ha simulated forest with different stages of succession. The following rows show the TCH-to-AGB
328
relationship with each record representing one 20-m, 50-m or 100-m plot, respectively, for 2) 1,400 ha of undisturbed
329
simulated forest (green), 3) 1,400 ha of fire-disturbed and 1,400 ha of regularly logged simulated forest (red) and 4) the
330
curves of the best power law fits.
331
21 332
Fig. 6: Aboveground biomass (AGB) as a function of top-of-canopy height (TCH) from 10-m pixel resolution (CHM) for different
333
plot sizes. All data was derived from FORMIND and lidar simulations. 1) The first row demonstrates the sampling approach.
334
Shown is a scene of 9 ha simulated forest with different stages of succession. The following rows show the TCH-to-AGB
335
relationship with each record representing one 20-m, 50-m or 100-m plot, respectively, for 2) 1,400 ha of undisturbed
336
simulated forest (green), 3) 1,400 ha of fire-disturbed and 1,400 ha of regularly logged simulated forest (red) and 4) the
337
curves of the best power law fits.
338 339
22
The general trends were that the nRMSE of the TCH-based AGB predictions increased with decreasing 340
plot size and with increasing pixel size (Fig. 7). The prediction accuracy at each scale was better for the 341
undisturbed forest dataset than for the disturbed forest dataset, indicated by generally lower nRMSE for 342
each plot size and pixel size combination for the undisturbed forest as compared to the disturbed forest 343
(Fig. 7). For the disturbed dataset and large plot sizes (100 and 200 m), we observed slightly better 344
prediction accuracies at medium pixel resolutions (5 and 10 m) than at fine pixel resolutions (1 and 2 m).
345
The analysis shows that to achieve, a plot-level biomass estimation error < 10%, plot sizes of ≥ 100 m are 346
required. At such plot sizes, any pixel size would be sufficient to predict AGB for undisturbed forests with 347
the desired accuracy, but for disturbed forests, the errors exceed 10% and increase strongly at pixel sizes 348
≥ 20 m. 349
350
Fig. 7: Normalized root mean square errors (nRMSE) [%] of power law models that describe the relationship between
351
aboveground biomass (AGB) and top-of-canopy height (TCH) at different plot scales and different pixel resolutions for
352
undisturbed and disturbed simulated forest. For pixel sizes of 1 and 10 m, the decrease in nRMSE with increasing plot size is
353
shown on the right side.
354 355
23 3.3 Biomass prediction based on various lidar metrics 356
In addition to TCH, we analyzed 21 other metrics concerning their capability to predict biomass using 357
power law equations. For this analysis, we no longer distinguished between the different disturbance 358
regimes and pooled all forest stands. Fig. 8 shows nRMSE values for all lidar metrics, for which it was 359
possible to fit a power law model, at the plot scales of 100 and 20 m. From left to right, the metrics are 360
sorted by increasing nRMSE at the 100-m plot size. The figure shows that the best ten metrics are all 361
measures of forest height. Vegetation density metrics (e.g., NAGR/NGR and FCC) and vertical heterogeneity 362
metrics (e.g., SD and Shannon Index) were less accurate AGB predictors than height metrics. The best 363
predictions at large plot scales were achieved by TCH (10 m) and TCH (5 m), whereas at small plot scales 364
RH75, MCH, QMCH and TCH (1 m) were the most accurate predictors. We could not find any relationship 365
between AGB and CV of height, profile skewness or P:H ratio. The Shannon Index of the profiles only 366
showed a relationship with AGB for plot sizes ≥ 50 m. Scatter plots of a selection of metrics against AGB 367
can be found in Fig. S12, nRMSE values for all metrics at all plot scales are displayed in Fig. S13 and 368
detailed statistics and the coefficients of all fit power laws are listed in Tab. S2.
369
370
Fig. 8: Normalized root mean square errors (nRMSE) [%] of power law models that describe the relationship between
371
aboveground biomass (AGB) and various lidar metrics (for explanations of the abbreviations, please refer to the main text
372
and Tab. 1) at plot scales of 100 and 20 m, respectively. From left to right, the metrics are sorted by increasing nRMSE at the
373
100-m plot size. Whether certain metrics were derived from point clouds (PC) or from canopy-height-models (CHM) is
374
indicated in brackets. This analysis was based on pooled (undisturbed and disturbed) simulated forest data and lidar
375
simulations. Missing bars indicate that no power law model could be fit at the 20-m plot size.
376 377
24 4. Discussion
378 379
This study demonstrated a new approach for simulating 3D lidar point clouds of forest stands and for 380
investigating structural lidar metrics for their relationship with AGB of a tropical forest using forest 381
simulations. We explored the accuracy of AGB predictions based on various lidar metrics, spatial scales 382
and considering undisturbed and disturbed forest plots.
383 384
4.1 Lidar simulations 385
Unlike other lidar simulation approaches that use detailed radiative transfer theory (Sun et al., 1993; Ni- 386
Meister et al., 2001; Kotchenova et al., 2003; Goodwin et al., 2007) or explicit 3D models of trees and ray 387
tracing (Disney et al., 2010; Endo et al., 2012), our method requires only a minimal parameter set to 388
efficiently compute synthetic lidar point clouds for large areas. Under simple assumptions, e.g., one DBH- 389
to-height and DBH-to-crown-diameter allometry, a constant crown length proportion, cylindrical crowns 390
shapes and a homogeneous leaf area density within crowns, the lidar model was able to reproduce the 391
vertical lidar profiles of different 9-ha subplots within the 50-ha BCI megaplot to an overlap of 87%. An 392
extinction factor kNIR of approximately 0.2 was suggested by empirical measurements (Jones, 2013) and 393
theoretical considerations (Campbell & Norman, 2012; Tang et al., 2012) and could be confirmed by our 394
inverse modeling tests.
395
Airborne and simulated profiles for the 9-ha subplots matched well in general. They diverged most in the 396
upper canopy, where the DBH-to-height allometry led to an overestimation of high trees. Frequencies of 397
ground returns of simulated profiles were approximately 25% lower than for the airborne data, which 398
could be adjusted by choosing another lidar return probability P0 for ground voxels. Because the exact 399
size of the ground return peak does not affect most of the lidar metrics, we did not treat ground voxels 400
differently than canopy voxels in this study. It should also be noted that simulated lidar profiles 401
25
(inventory- and FORMIND-based) contain only returns from trees and ground. Non-woody vegetation 402
such as shrubs and lianas may contribute to the airborne lidar profiles, particularly near ground, whereas 403
they are absent in the simulations.
404 405
4.2 Biomass prediction from lidar height 406
For the simulated BCI lidar dataset, TCH at various pixel resolutions performed better than any other 407
lidar metric for biomass predictions. The lowest AGB prediction errors (< 10%) were found for large 408
mapping units (plot sizes of 100 and 200 m) with TCH derived from CHMs with pixel sizes of 5 to 20 m.
409
For the smaller mapping units of 50 m, 33 m and 20 m, the minimal achievable errors from any metric 410
were 15%, 23% and 33%, respectively. At those scales, the high pixel resolution TCH, RH75 or point- 411
cloud-based MCH and QMCH led to slightly smaller errors than TCH of medium pixel resolution. The 412
finding that medium pixel resolution CHMs are sufficient to make highly accurate AGB predictions at the 413
1-ha scale is encouraging for spaceborne biomass mapping efforts on the global scale. The generation of 414
high-resolution information (e.g., pixel size of 1 m) requires airborne laser scanning campaigns, whereas 415
medium resolutions can be derived from satellites. The synthetic aperture radar satellite system 416
TanDEM-X can provide forest heights closely correlated to TCH at a resolution of 10 m (referred to as 417
H100 in the radar literature; Kugler et al., 2014; Lee & Fatoyinbo, 2015). Future sensors, such as GEDI 418
(http://science.nasa.gov/missions/gedi/) and Tandem-L (https://www.tandem-l.de/), will provide data of 419
similar horizontal resolution (20 to 50 m) and improved vertical resolution. Thus, TCH as well as MCH and 420
RH75 of the vertical profiles are promising metrics for estimating AGB using these sensors. The analysis 421
also showed that sensors that only provide maximum height at the coarse resolution of 100 m lead to 422
AGB estimation errors of > 25%. It appears highly plausible that CHMs with pixels sizes around 10 m that 423
correspond to the dimensions of the objects of interest, namely crowns of medium to large trees, which 424
contribute most to the total AGB, are a good data source for AGB inference. High-resolution data such as 425
26
1-m pixel CHMs or the full point cloud have the advantage of providing detailed information on crown 426
architecture and small gaps, but this information might only be additional noise in the signal for stand 427
level AGB and may not be necessary for large-scale mapping.
428 429
4.3 The role of structural metrics 430
Metrics of vertical heterogeneity (e.g., standard deviation or Shannon Index) and vegetation density 431
(e.g., NAGR/NGR or FCC) showed weaker relationships with AGB than most of the height metrics. Hence, 432
these metrics might not be the optimal choice as single AGB predictors. However, considering vegetation 433
structure in addition to mean height could potentially improve AGB estimations. Several approaches 434
have been suggested to improve power-law-based lidar-to-AGB models by considering additional 435
predictors. These predictors include horizontal and vertical structure indices (Tello et al., 2015) and 436
texture metrics of the CHM (Abdullahi et al., 2016). Finally, when thinking beyond AGB stock prediction 437
and towards the study of forest dynamics and disturbances based on remote sensing, structural metrics 438
may become very important. The Shannon Index of the lidar profile has been previously associated with 439
productivity and mortality (Stark et al., 2012), and gap fraction and size distribution may provide 440
information about disturbances (Lobo & Dalling, 2014).
441 442
4.4 Prediction errors 443
For all tested lidar metrics, we observed the tendency for the prediction errors to decrease with 444
increasing plot scale. This pattern has been reported and quantified previously for MCH (Asner et al., 445
2010; Mascaro et al., 2011b), QMCH (Chen et al. 2016) and TCH (Köhler & Huth, 2010; Asner & Mascaro, 446
2014) and in general for the situation in which remote sensing footprints and ground plot extents do not 447
fully match (Réjou-Méchain et al., 2014). In our analysis, the spatial locations and extents of ground plots 448
and remote sensing data matched perfectly, because they were based on simulations. Also there was no 449
27
displacement of crowns from stem locations. Thus, our dataset is free of geolocation errors and the 450
observed residuals in the lidar-to-AGB relationships can be attributed to the following sources of 451
uncertainty: 1) the highly clumped biomass distribution on the ground, i.e., the majority of biomass is 452
localized in tree trunks at specific positions with empty space in between, whereas remote sensing 453
signals capture the tree crowns, which are spread around the trunk positions; 2) edge effects of 454
overhanging tree crowns with trunk positions and thus biomass being located outside the focal plot area;
455
3) the general variability among trees with respect to their geometries and wood densities; and 4) the 456
undergrowth vegetation that is obscured by the upper canopy and not detected by the remote sensing 457
sensor. The error caused by 1) should decrease with increasing plot size due to the decrease in biomass 458
variability (Fig. 3) and the decreasing influence of single large trees. The error caused by 2) should 459
decrease with increasing core area to edge length ratio. The error caused by 3) should decrease because 460
differences at the individual tree level average out with increasing plot size. Only errors caused by 4) can 461
be expected to be scale-independent. Using a crown-distributed instead of a stem-localized biomass 462
distribution as ground truth has been shown to reduce estimation errors (Mascaro et al., 2011b).
463
However, the actual biomass distribution in a forest is expected to be closer to being stem-localized than 464
(uniformly) crown-distributed. Thus, reducing errors by assuming crown-distributed biomass does not 465
necessarily lead to more accurate biomass maps. Our modeling approach may allow future studies to 466
gain a closer look at the contributions of the separate error sources by switching them off one at a time.
467
Different lidar metrics showed different changes in errors across scales: e.g., in moving from large to 468
small plots, the errors of TCH20, TCH33 and the Shannon Index increased much faster than for other 469
metrics with similar errors at the 200-m scale (Fig. 8 and S13). For the Shannon Index, the relationship 470
with AGB was entirely lost at scales smaller than 50 m.
471 472
4.5 Linking remote sensing with dynamic forest models 473
28
Despite the great potential of the proposed approach, relatively few studies have linked remote sensing 474
and forest modeling. Applications include model initialization (Ranson et al., 2001; Hurtt et al., 2004), 475
model parameterization (Falkowski et al., 2010), remote sensing calibration (Köhler & Huth, 2010; Palace 476
et al., 2015), error quantification (Hurtt et al., 2010; Frazer et al., 2011) and the understanding of large- 477
scale ecosystem patterns and processes (Shugart et al., 2015). Our study is the first to demonstrate how 478
remote sensing simulations combined with a dynamic forest model can provide remote sensing metrics 479
over the full range of disturbance-induced successional stages, which is particularly useful for tropical 480
forests where available field data is limited. The lidar-to-AGB relationships can differ between 481
disturbance types because one type (e.g., fire) might cause mosaics of surviving trees and bare ground, 482
whereas another type (e.g., selective logging) might cause a height degradation throughout the entire 483
study area. Horizontal heterogeneities, such as those caused by fires, are particularly problematic when 484
lidar metrics are aggregated over larger areas. Thus, the disturbance regime of a region and the presence 485
of the described phenomena should be taken into account when deciding which metric and resolution to 486
choose for biomass mapping. Modeling can be one way to explore these effects in greater detail.
487
An important condition for combining a forest model and remote sensing is the structural realism of the 488
model in the relevant aspects. Overall, our model was able to reproduce forest attributes and literature 489
values well. Previous studies on BCI that linked AGB at the 1-ha scale to MCH derived from airborne lidar 490
scans reported RMSE values of 17 tCarbon/ha (Mascaro et al., 2011a) and 28.9 tAGB/ha (Meyer et al., 2013) 491
in agreement with the value of 27.1 tAGB/ha we obtained for the pooled simulated dataset (Tab. S2). A 492
noteworthy deviation between the simulation data and reference data was that for comparable AGB 493
values the simulated TCH was higher than the airborne TCH, particularly at the upper end of the AGB and 494
TCH ranges (described in detail in supplements). We believe that this deviation was primarily caused by 495
the simple tree geometries used in the forest model. Using only one general DBH-to-height allometry for 496
all trees might be suboptimal if the aim is to reproduce the natural height heterogeneity of the upper 497
29
canopy at all scales. In our simulations, too many trees reached the maximum possible height of 55 m, 498
which is an exceptional height on BCI observed for only one tree in the airborne lidar CHM. Hurtt et al.
499
(2004) encountered a similar problem with large trees. In their case, model-derived canopy heights were 500
restrained to a maximum, whereas observed lidar heights exceeded that limit. Therefore, one potential 501
improvement for future model parameterizations would be to consider asymptotic instead of power law 502
DBH-to-height allometries and allow for a certain plasticity of modeled heights and crown diameters. The 503
sensitivity analysis about model assumptions showed that the alternative scenario using an asymptotic 504
tree height allometry led to slight increases in R² and decreases in nRMSE of the stand height to biomass 505
relationship (S16-S18). Recent advances in individual tree delineation from airborne lidar (Duncanson et 506
al., 2014; Ferraz et al., 2016) and terrestrial laser scanning (Raumonen et al., 2013) have the potential to 507
improve our understanding of tree allometries and the structural realism of forest models. When models 508
are able to reproduce observed patterns in the relationship between remote sensing metrics and static 509
biomass stocks, we can move forward using the presented methodology to explore dynamic changes of 510
biomass stocks.
511 512
5. Conclusion 513
514
This study introduced a novel approach for coupling remote sensing simulations with a dynamic forest 515
model to derive structure-to-biomass relationships for a tropical forest, including disturbed stands. The 516
lidar model was validated successfully with airborne and census reference data from Barro Colorado 517
Island. The model proved its capacity for efficient and realistic lidar point cloud simulations for large, 518
simulated forest stands. Virtual forest inventory datasets were generated with a forest model and 519
sampled with the lidar simulation model. The results provide a comprehensive overview of biomass 520
30
estimation errors for a wide range of lidar metrics and spatial scales and may guide decisions on which 521
metric to choose for a given remote sensing data structure (e.g., point clouds, vertical profiles, canopy 522
height models). It was found that height-to-biomass relationships were similar for undisturbed and 523
disturbed forest, but errors were larger for the latter. Furthermore, we found that top-of-canopy height 524
was an accurate biomass predictor even if pixel resolutions were only 10 to 20 m. Such resolutions could 525
be derived at large scale from spaceborne sensors.
526 527
Acknowledgments 528
529
We thank J. Dalling for providing the lidar data and the Smithsonian Tropical Research Institute for 530
providing the census data for BCI. The BCI forest dynamics research project was founded by S.P. Hubbell 531
and R.B. Foster and is now managed by R. Condit, S. Lao, and R. Perez under the Center for Tropical 532
Forest Science and the Smithsonian Tropical Research in Panama. Numerous organizations have 533
provided funding, principally the U.S. National Science Foundation, and hundreds of field workers have 534
contributed. This study was conducted with funding by the German Federal Ministry for Economic Affairs 535
and Energy (BMWi) under the funding reference 50EE1416. RF and AH were supported by the HGF- 536
Helmholtz Alliance “Remote Sensing and Earth System Dynamics”. We thank two reviewers for their 537
constructive comments on our paper.
538 539
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